Specifically, the transistor properties are different, and so are the properties of the tiny metal wires connecting the transistors together. Once you get to the design phase where you're dealing with individual transistors (for analog this is right off the bat; for digital it's once you get to place & route), you spend thousands of hours simulating the behavior of the analog circuits, or the effects of the particular arrangement of digital logic gates, to make sure everything works. When the transistor and wire properties change, you at minimum have to repeat all of that verification
Sometimes, the new process is different enough that an old design no longer works, and it takes a lot of engineering effort to fix it. Other times, a few small tweaks are enough. In some cases, particularly for digital-only ICs, the foundry will validate the migration between two processes, essentially saying, "we guarantee the IC you already designed will just work in this new process". Smaller companies might just go with it and accept any yield fallout, but bigger companies like Qualcomm would probably do their own independent verification.